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Proof step 3 from proof refine-get-block-free-size (previous step)

# lpt = # avol, # lpt0 = # avol, keyset(gch) = gc-heap(lpt, log1), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt, gstore, ginval), abs-istore(avol, lpt, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt), buf-ro-rw-mode(pstate = readonly, bleb, lpt, avol), bufs-log-only(bleb, log1, lpt), flash-lpt-cons(lpt0, istore0, gstore0), freelist-cons(lpt, freelist), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), log-group-block(log1, lpt), lpt-free-unref(lpt), lpt-free-unref(lpt0), lpt-leb-size(lpt), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt0, log1), istore0 ⊑ istore, ¬ dups(log1), isbuf → synced(avol), pstate = unbuffered → bleb = nobuffer, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate.index? → pstate.lnum ∈ istore, pstate = unbuffered → isbuf ⊦ ⟪persistence_get_block_free_size#(lpt, LEB_SIZE, adr0, m, log1, avol, lpt0, ns0, bleb, pstate = readonly; ; n)⟫ ⟨apersistence_get_block_free_size#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0, pstate, isbuf; ; n0)⟩ ( (isbuf → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ n = n0)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 4:
# lpt1 = # avol, # lpt2 = # avol, isbuf ↔ pstate = readonly, adr = adr0, bleb0 = bleb, keyset(gch) = gc-heap(lpt2, log1), log = log1, lpt = lpt1, lpt0 = lpt2, m0 = LEB_SIZE, ns = ns0, remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems log1 ∩ ginval = ∅, dom gstore0 ∪ elems log1 = dom gstore ∪ ginval, ginval < # avol, abs-gstore(avol, lpt2, gstore, ginval), abs-istore(avol, lpt2, istore), awbuf-inv(avol, bleb), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(pstate = readonly, bleb, lpt2, avol), bufs-log-only(bleb, log1, lpt2), flash-lpt-cons(lpt1, istore0, gstore0), freelist-cons(lpt2, freelist), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), log-group-block(log1, lpt2), lpt-free-unref(lpt1), lpt-free-unref(lpt2), lpt-leb-size(lpt1), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt1, log1), istore0 ⊑ istore, pstate = unbuffered → isbuf0, pstate.index? → pstate.lnum ∈ istore, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last ∧ pstate.lnum ∈ gstore, pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum), pstate = unbuffered → bleb = nobuffer, isbuf0 → synced(avol) ⊦ ⟪let bleb = ? in {awbuf_get_buf#(adr, m, log, avol, lpt, ns, bleb0, isbuf; ; bleb); if bleb = nobuffer then n := 0 else n := m0 - lpt0[bleb.leb].size}⟫ ⟨apersistence_get_block_free_size#(adr0, istore, istore0, ginval, gstore, gstore0, log1, m, ns0, pstate, isbuf0; ; n0)⟩ ( (isbuf0 → synced(avol)) ∧ (pstate = unbuffered → bleb = nobuffer) ∧ (pstate ≠ unbuffered ∧ pstate ≠ readonly → bleb = buffered(pstate.lnum)) ∧ n = n0), dups(log1)

Rule argument

pos: right 1

Additional information

Used simplifier rules: persistence_get_block_free_size# (LPT, LEBSIZE, WROOTADR, WMAXINO, WLOG, WVOL, WLPT, WORPHANS, WBUFLEB, AROFS ; ; N ) {let WBUFLEB0 = ? in {awbuf_get_buf# (WROOTADR, WMAXINO, WLOG, WVOL, WLPT, WORPHANS, WBUFLEB, AROFS ; ; WBUFLEB0); if WBUFLEB0 = nobuffer then N := 0 else N := LEBSIZE - LPT[WBUFLEB0.leb].size} };